: : : : : : : : I believe it to be just another case
of choosing an animal to illustrate a point - eg 'sick as a parrot', 'dog-tired'.
The example is particularly crude, because I've always understood that there's
a missing word, indicating that things are so trivial as to be not worth caring
about. 'I don't give a monkey's f**k'.

:
: : : : Tinkers' cuss is probably the oldest followed by monkey's toss, which
I think started as a sailor's expression.
: : : : : The coarse version - "I
don't give a monkey's toss" (i.e. the ejaculate of a monkey has no value) was
sanitised to the other versions in particular "uncle" and as it was widely understood
just "a monkey's" which is the essence of the phrase. I think MT had currency
for a long while, but more recently the shortened version has been more popular
vernacular.
: : : : : Modern equivalents being "a flying" as in "flying fuck"
or "'kin!" which gets used to avoid offence - as in 'kin'ell! ("Fucking hell!")

:
: : : : I don't know how best that can be verified, but I do think that monkey's
toss followed on in the spirit of tinker's cuss and then became sanitised.

:
Really? Do you remember the context by any chance, or better yet, know the page
number?

In the 1945 Viking Press edition, the one that says "This Edition Is
Produced in Full Compliance with All War Production Board Conservation Orders,"
it's page 91.

Near end of Chapter 14:
From up near the station . . . the
watchman . . . shouted at them . . . "Don't you know you can't lay around here?
You got to get off. This is private property!"
. . . At last in slow motion
one of the soldiers turned his head . . . "Why don't you take a flying fuggut
the moon?" he said kindly and he turned back to look at the girl.